The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles

Details The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles

2002-01-25

arxiv.org/abs/math/0201244v1

Mathematics

Algebraic Geometry

22 pages, 3 figures. To appear in: Journal of Algebraic Geometry

Scientific paper

In this paper we give a geometrical interpretation of an extension of mixed Hodge structures (MHS) obtained from the canonical MHS on the group ring of the fundamental group of a hyperelliptic curve modulo the fourth power of its augmentation ideal. We show that the class of this extension coincides with the regulator image of a canonical higher cycle in a hyperelliptic jacobian. This higher cycle was introduced and studied by Collino.

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